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Analysis of Hexagonal Grid Finite Difference Methods for Anisotropic Laplacian Related Equations

Part of: Partial differential equations, boundary value problems Basic linear algebra

Published online by Cambridge University Press:  20 June 2017

Daniel Lee
Daniel Lee*
Affiliation:
Department of Applied Mathematics, Tunghai University, Taichung 40704, Taiwan, Republic of China
*
*Corresponding author. Email address:danlee@thu.edu.tw (D. Lee)
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Abstract

Hexagonal grids are valuable in two-dimensional applications involving Laplacian. The methods and analysis are investigated in current work in both linear and nonlinear problems related to anisotropic Laplacian. Ordinary and compact hexagonal grid finite difference methods are developed by elementary arguments, and then analyzed by perturbation for standard Laplacian. In the anisotropic case, analysis is done through reduction to the standard one by using Fourier vectors of mixed types. These hexagonal seven-point methods, with established theoretic stabilities and accuracies, are numerically confirmed in linear and semi-linear anisotropic Poisson problems, and can be applied also in time-dependent problems and in many applications in two-dimensional irregular domains.

Keywords

Compact schemehexagonal grid methodmatrix perturbationfourier vectors

MSC classification

Secondary: 65N06: Finite difference methods 65N12: Stability and convergence of numerical methods 65N22: Solution of discretized equations 15A18: Eigenvalues, singular values, and eigenvectors 15A63: Quadratic and bilinear forms, inner products
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 3 , August 2017 , pp. 562 - 596
Copyright
Copyright © Global-Science Press 2017 

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